An asymmetric multiparameter CCR flow

Sundar, S.

doi:10.1090/proc/15450

An asymmetric multiparameter CCR flow
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Proc. Amer. Math. Soc. 149 (2021), 3037-3044 Request permission

Abstract:

In this note, we show that the opposite of a multiparameter CCR flow is a CCR flow. We also exhibit an example of a multiparameter CCR flow which is not cocycle conjugate to its opposite. This is in sharp contrast to the one parameter situation.

References

Anbu Arjunan, R. Srinivasan, and S. Sundar, E-semigroups over closed convex cones, J. Operator Theory 84 (2020), no. 2, 289–322. MR 4157363, DOI 10.7900/jot.2018sep17.2271
Anbu Arjunan and S. Sundar, CCR flows associated to closed convex cones, Münster J. Math. 13 (2020), no. 1, 115–143. MR 4077100, DOI 10.17879/32109554453
William Arveson, Noncommutative dynamics and $E$-semigroups, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1978577, DOI 10.1007/978-0-387-21524-2
R. G. Douglas, On extending commutative semigroups of isometries, Bull. London Math. Soc. 1 (1969), 157–159. MR 246153, DOI 10.1112/blms/1.2.157
Joachim Hilgert and Karl-Hermann Neeb, Wiener-Hopf operators on ordered homogeneous spaces. I, J. Funct. Anal. 132 (1995), no. 1, 86–118. MR 1346219, DOI 10.1006/jfan.1995.1101
Marcelo Laca and Iain Raeburn, Extending multipliers from semigroups, Proc. Amer. Math. Soc. 123 (1995), no. 2, 355–362. MR 1227519, DOI 10.1090/S0002-9939-1995-1227519-6
S. P. Murugan and S. Sundar, On the existence of $E_0$-semigroups—the multiparameter case, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21 (2018), no. 2, 1850007, 20. MR 3819807, DOI 10.1142/S0219025718500078
S. P. Murugan and S. Sundar, $E_0^{P}$-semigroups and Product systems, arXiv:1706.03928.
S. Sundar, Arveson’s characterisation of CCR flows: the multiparameter case, J. Funct. Anal. 280 (2021), no. 1, Paper No. 108802, 44. MR 4157679, DOI 10.1016/j.jfa.2020.108802
Boris Tsirelson, From random sets to continuous tensor products: answers to three questions of W. Arveson, arXiv:math.FA:0001070.
Boris Tsirelson, Non-isomorphic product systems, Advances in quantum dynamics (South Hadley, MA, 2002) Contemp. Math., vol. 335, Amer. Math. Soc., Providence, RI, 2003, pp. 273–328. MR 2029632, DOI 10.1090/conm/335/06017